/* linalg/gsl_linalg.h
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman, Brian Gough
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

#ifndef __GSL_LINALG_H__
#define __GSL_LINALG_H__

#include <gsl/gsl_mode.h>
#include <gsl/gsl_permutation.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_matrix.h>

#undef __BEGIN_DECLS
#undef __END_DECLS
#ifdef __cplusplus
#define __BEGIN_DECLS extern "C" {
#define __END_DECLS }
#else
#define __BEGIN_DECLS		/* empty */
#define __END_DECLS		/* empty */
#endif

__BEGIN_DECLS typedef enum
{
  GSL_LINALG_MOD_NONE = 0,
  GSL_LINALG_MOD_TRANSPOSE = 1,
  GSL_LINALG_MOD_CONJUGATE = 2
}
gsl_linalg_matrix_mod_t;


/* Note: You can now use the gsl_blas_dgemm function instead of matmult */

/* Simple implementation of matrix multiply.
 * Calculates C = A.B
 *
 * exceptions: GSL_EBADLEN
 */
//int gsl_linalg_matmult (const gsl_matrix * A,
//                       const gsl_matrix * B,
//                      gsl_matrix * C);
//

/* Simple implementation of matrix multiply.
 * Allows transposition of either matrix, so it
 * can compute A.B or Trans(A).B or A.Trans(B) or Trans(A).Trans(B)
 *
 * exceptions: GSL_EBADLEN
 */
//int gsl_linalg_matmult_mod (const gsl_matrix * A,
//                           gsl_linalg_matrix_mod_t modA,
//                          const gsl_matrix * B,
//                          gsl_linalg_matrix_mod_t modB,
//                          gsl_matrix * C);
//
/* Calculate the matrix exponential by the scaling and
 * squaring method described in Moler + Van Loan,
 * SIAM Rev 20, 801 (1978). The mode argument allows
 * choosing an optimal strategy, from the table
 * given in the paper, for a given precision.
 *
 * exceptions: GSL_ENOTSQR, GSL_EBADLEN
 */
int gsl_linalg_exponential_ss (const gsl_matrix * A,
			       gsl_matrix * eA, gsl_mode_t mode);


/* Householder Transformations */

double gsl_linalg_householder_transform (gsl_vector * v);
gsl_complex gsl_linalg_complex_householder_transform (gsl_vector_complex * v);

int gsl_linalg_householder_hm (double tau,
			       const gsl_vector * v, gsl_matrix * A);

int gsl_linalg_householder_mh (double tau,
			       const gsl_vector * v, gsl_matrix * A);

int gsl_linalg_householder_hv (double tau,
			       const gsl_vector * v, gsl_vector * w);

int gsl_linalg_householder_hm1 (double tau, gsl_matrix * A);

int gsl_linalg_complex_householder_hm (gsl_complex tau,
				       const gsl_vector_complex * v,
				       gsl_matrix_complex * A);

int gsl_linalg_complex_householder_hv (gsl_complex tau,
				       const gsl_vector_complex * v,
				       gsl_vector_complex * w);

/* Singular Value Decomposition

 * exceptions: 
 */

int
gsl_linalg_SV_decomp (gsl_matrix * A,
		      gsl_matrix * V, gsl_vector * S, gsl_vector * work);

int
gsl_linalg_SV_decomp_mod (gsl_matrix * A,
			  gsl_matrix * X,
			  gsl_matrix * V, gsl_vector * S, gsl_vector * work);

int gsl_linalg_SV_decomp_jacobi (gsl_matrix * A,
				 gsl_matrix * Q, gsl_vector * S);

int
gsl_linalg_SV_solve (const gsl_matrix * U,
		     const gsl_matrix * Q,
		     const gsl_vector * S,
		     const gsl_vector * b, gsl_vector * x);


/* LU Decomposition, Gaussian elimination with partial pivoting
 */

int gsl_linalg_LU_decomp (gsl_matrix * A, gsl_permutation * p, int *signum);

int gsl_linalg_LU_solve (const gsl_matrix * LU,
			 const gsl_permutation * p,
			 const gsl_vector * b, gsl_vector * x);

int gsl_linalg_LU_svx (const gsl_matrix * LU,
		       const gsl_permutation * p, gsl_vector * x);

int gsl_linalg_LU_refine (const gsl_matrix * A,
			  const gsl_matrix * LU,
			  const gsl_permutation * p,
			  const gsl_vector * b,
			  gsl_vector * x, gsl_vector * residual);

int gsl_linalg_LU_invert (const gsl_matrix * LU,
			  const gsl_permutation * p, gsl_matrix * inverse);

double gsl_linalg_LU_det (gsl_matrix * LU, int signum);
double gsl_linalg_LU_lndet (gsl_matrix * LU);
int gsl_linalg_LU_sgndet (gsl_matrix * lu, int signum);

/* Complex LU Decomposition */

int gsl_linalg_complex_LU_decomp (gsl_matrix_complex * A,
				  gsl_permutation * p, int *signum);

int gsl_linalg_complex_LU_solve (const gsl_matrix_complex * LU,
				 const gsl_permutation * p,
				 const gsl_vector_complex * b,
				 gsl_vector_complex * x);

int gsl_linalg_complex_LU_svx (const gsl_matrix_complex * LU,
			       const gsl_permutation * p,
			       gsl_vector_complex * x);

int gsl_linalg_complex_LU_refine (const gsl_matrix_complex * A,
				  const gsl_matrix_complex * LU,
				  const gsl_permutation * p,
				  const gsl_vector_complex * b,
				  gsl_vector_complex * x,
				  gsl_vector_complex * residual);

int gsl_linalg_complex_LU_invert (const gsl_matrix_complex * LU,
				  const gsl_permutation * p,
				  gsl_matrix_complex * inverse);

gsl_complex gsl_linalg_complex_LU_det (gsl_matrix_complex * LU, int signum);

double gsl_linalg_complex_LU_lndet (gsl_matrix_complex * LU);

gsl_complex gsl_linalg_complex_LU_sgndet (gsl_matrix_complex * LU,
					  int signum);

/* QR decomposition */

int gsl_linalg_QR_decomp (gsl_matrix * A, gsl_vector * tau);

int gsl_linalg_QR_solve (const gsl_matrix * QR,
			 const gsl_vector * tau,
			 const gsl_vector * b, gsl_vector * x);

int gsl_linalg_QR_svx (const gsl_matrix * QR,
		       const gsl_vector * tau, gsl_vector * x);

int gsl_linalg_QR_lssolve (const gsl_matrix * QR,
			   const gsl_vector * tau,
			   const gsl_vector * b,
			   gsl_vector * x, gsl_vector * residual);


int gsl_linalg_QR_QRsolve (gsl_matrix * Q,
			   gsl_matrix * R,
			   const gsl_vector * b, gsl_vector * x);

int gsl_linalg_QR_Rsolve (const gsl_matrix * QR,
			  const gsl_vector * b, gsl_vector * x);

int gsl_linalg_QR_Rsvx (const gsl_matrix * QR, gsl_vector * x);

int gsl_linalg_QR_update (gsl_matrix * Q,
			  gsl_matrix * R,
			  gsl_vector * w, const gsl_vector * v);

int gsl_linalg_QR_QTvec (const gsl_matrix * QR,
			 const gsl_vector * tau, gsl_vector * v);

int gsl_linalg_QR_Qvec (const gsl_matrix * QR,
			const gsl_vector * tau, gsl_vector * v);

int gsl_linalg_QR_unpack (const gsl_matrix * QR,
			  const gsl_vector * tau,
			  gsl_matrix * Q, gsl_matrix * R);

int gsl_linalg_R_solve (const gsl_matrix * R,
			const gsl_vector * b, gsl_vector * x);

int gsl_linalg_R_svx (const gsl_matrix * R, gsl_vector * x);


/* Q R P^T decomposition */

int gsl_linalg_QRPT_decomp (gsl_matrix * A,
			    gsl_vector * tau,
			    gsl_permutation * p,
			    int *signum, gsl_vector * norm);

int gsl_linalg_QRPT_decomp2 (const gsl_matrix * A,
			     gsl_matrix * q, gsl_matrix * r,
			     gsl_vector * tau,
			     gsl_permutation * p,
			     int *signum, gsl_vector * norm);

int gsl_linalg_QRPT_solve (const gsl_matrix * QR,
			   const gsl_vector * tau,
			   const gsl_permutation * p,
			   const gsl_vector * b, gsl_vector * x);


int gsl_linalg_QRPT_svx (const gsl_matrix * QR,
			 const gsl_vector * tau,
			 const gsl_permutation * p, gsl_vector * x);

int gsl_linalg_QRPT_QRsolve (const gsl_matrix * Q,
			     const gsl_matrix * R,
			     const gsl_permutation * p,
			     const gsl_vector * b, gsl_vector * x);

int gsl_linalg_QRPT_Rsolve (const gsl_matrix * QR,
			    const gsl_permutation * p,
			    const gsl_vector * b, gsl_vector * x);

int gsl_linalg_QRPT_Rsvx (const gsl_matrix * QR,
			  const gsl_permutation * p, gsl_vector * x);

int gsl_linalg_QRPT_update (gsl_matrix * Q,
			    gsl_matrix * R,
			    const gsl_permutation * p,
			    gsl_vector * u, const gsl_vector * v);

/* Cholesky Decomposition */

int gsl_linalg_cholesky_decomp (gsl_matrix * A);

int gsl_linalg_cholesky_solve (const gsl_matrix * cholesky,
			       const gsl_vector * b, gsl_vector * x);

int gsl_linalg_cholesky_svx (const gsl_matrix * cholesky, gsl_vector * x);

/* Symmetric to symmetric tridiagonal decomposition */

int gsl_linalg_symmtd_decomp (gsl_matrix * A, gsl_vector * tau);

int gsl_linalg_symmtd_unpack (const gsl_matrix * A,
			      const gsl_vector * tau,
			      gsl_matrix * Q,
			      gsl_vector * diag, gsl_vector * subdiag);

int gsl_linalg_symmtd_unpack_T (const gsl_matrix * A,
				gsl_vector * diag, gsl_vector * subdiag);

/* Hermitian to symmetric tridiagonal decomposition */

int gsl_linalg_hermtd_decomp (gsl_matrix_complex * A,
			      gsl_vector_complex * tau);

int gsl_linalg_hermtd_unpack (const gsl_matrix_complex * A,
			      const gsl_vector_complex * tau,
			      gsl_matrix_complex * Q,
			      gsl_vector * diag, gsl_vector * sudiag);

int gsl_linalg_hermtd_unpack_T (const gsl_matrix_complex * A,
				gsl_vector * diag, gsl_vector * subdiag);

/* Linear Solve Using Householder Transformations

 * exceptions: 
 */

int gsl_linalg_HH_solve (gsl_matrix * A, const gsl_vector * b,
			 gsl_vector * x);
int gsl_linalg_HH_svx (gsl_matrix * A, gsl_vector * x);

/* Linear solve for a symmetric tridiagonal system.

 * The input vectors represent the NxN matrix as follows:
 *
 *     diag[0]  offdiag[0]             0    ...
 *  offdiag[0]     diag[1]    offdiag[1]    ...
 *           0  offdiag[1]       diag[2]    ...
 *           0           0    offdiag[2]    ...
 *         ...         ...           ...    ...
 */
int gsl_linalg_solve_symm_tridiag (const gsl_vector * diag,
				   const gsl_vector * offdiag,
				   const gsl_vector * b, gsl_vector * x);

/* Linear solve for a nonsymmetric tridiagonal system.

 * The input vectors represent the NxN matrix as follows:
 *
 *       diag[0]  abovediag[0]              0    ...
 *  belowdiag[0]       diag[1]   abovediag[1]    ...
 *             0  belowdiag[1]        diag[2]    ...
 *             0             0   belowdiag[2]    ...
 *           ...           ...            ...    ...
 */
int gsl_linalg_solve_tridiag (const gsl_vector * diag,
			      const gsl_vector * abovediag,
			      const gsl_vector * belowdiag,
			      const gsl_vector * b, gsl_vector * x);


/* Linear solve for a symmetric cyclic tridiagonal system.

 * The input vectors represent the NxN matrix as follows:
 *
 *      diag[0]  offdiag[0]             0   .....  offdiag[N-1]
 *   offdiag[0]     diag[1]    offdiag[1]   .....
 *            0  offdiag[1]       diag[2]   .....
 *            0           0    offdiag[2]   .....
 *          ...         ...
 * offdiag[N-1]         ...
 */
int gsl_linalg_solve_symm_cyc_tridiag (const gsl_vector * diag,
				       const gsl_vector * offdiag,
				       const gsl_vector * b, gsl_vector * x);

/* Linear solve for a nonsymmetric cyclic tridiagonal system.

 * The input vectors represent the NxN matrix as follows:
 *
 *        diag[0]  abovediag[0]             0   .....  belowdiag[N-1]
 *   belowdiag[0]       diag[1]  abovediag[1]   .....
 *              0  belowdiag[1]       diag[2]
 *              0             0  belowdiag[2]   .....
 *            ...           ...
 * abovediag[N-1]           ...
 */
int gsl_linalg_solve_cyc_tridiag (const gsl_vector * diag,
				  const gsl_vector * abovediag,
				  const gsl_vector * belowdiag,
				  const gsl_vector * b, gsl_vector * x);


/* Bidiagonal decomposition */

int gsl_linalg_bidiag_decomp (gsl_matrix * A,
			      gsl_vector * tau_U, gsl_vector * tau_V);

int gsl_linalg_bidiag_unpack (const gsl_matrix * A,
			      const gsl_vector * tau_U,
			      gsl_matrix * U,
			      const gsl_vector * tau_V,
			      gsl_matrix * V,
			      gsl_vector * diag, gsl_vector * superdiag);

int gsl_linalg_bidiag_unpack2 (gsl_matrix * A,
			       gsl_vector * tau_U,
			       gsl_vector * tau_V, gsl_matrix * V);

int gsl_linalg_bidiag_unpack_B (const gsl_matrix * A,
				gsl_vector * diag, gsl_vector * superdiag);

/* Balancing */

int gsl_linalg_balance_columns (gsl_matrix * A, gsl_vector * D);


/* JM 140414 -- I've had to include a few definitions from gsl/gsl_cblas.h and gsl/gsl_blas_types.h here
   instead of including the files, as some of the variables conflicted with python */

typedef  enum CBLAS_TRANSPOSE   CBLAS_TRANSPOSE_t;
enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113};

/* we use this function to multiply matrices together and check if our populations matrix
   is a solution to the rate equations */
int  gsl_blas_dgemv (CBLAS_TRANSPOSE_t TransA,
                     double alpha,
                     const gsl_matrix * A,
                     const gsl_vector * X,
                     double beta,
                     gsl_vector * Y);


__END_DECLS
#endif /* __GSL_LINALG_H__ */
